Question

Every day a kindergarten class chooses randomly one of the 50 state flags to hang on the wall, without regard to previous choices. We are interested in the flags that are chosen on Monday, Tuesday and Wednesday of next week.
(a) Describe a sample space Ω and a probability measure P to model this experi- ment.
(b) What is the probability that the class hangs Wisconsin’s flag on Monday, Michi- gan’s flag on Tuesday, and California’s flag on Wednesday?
(c) What is the probability that Wisconsin’s flag will be hung at least two of the three days?

Answer 1

a)

The sample space S  is Flags of all 50 US states.

As, any of the flags are randomly chosen, Probability is calculated as,

P(X = x) = 1/50 for all x S

b)

As, the flag chosen on any day is independent of previous days, probability that the class hangs Wisconsin's flag on Monday, Michigan's flag on Tuesday, and California's flag on Wednesday

= (1/50) * (1/50) * (1/50) = 1/125000=1/(50)^3

c)

The probability that Wisconsin's flag will be hung at least two of the three days

= Probability that Wisconsin's flag will be hung on two days + Probability that Wisconsin's flag will be hung on three days

= ₃C₂ (1/50) * (1/50) * (49/50) +  ₃C₃ (1/50) * (1/50) *(1/50) {By binomial distribution formula)

= (147 / 125000 ) + (1/125000)

= 148 / 125000

= 37 / 31250 = 0.001184